Question

r=8cos(theta)+5sin(theta), convert the polar equation into a rectangular equation and then complete the square and determine the center radius...?

Help?! I missed the section, and am not getting anywhere with the text...

Answer 1

In your text, you should find a diagram similar to this one
http://en.wikipedia.org/wiki/File:Polar_to_cartesian.svg

If you label the endpoint of the rotating arm as either
(x,y) in rectangular and (r,Ø) in polar, then

x = rcosØ or cosØ = x/r
y = rsinØ or sinØ = y/r

also x^2 + y^2 = r^2, and tanØ = y/x

then in your equation r = 8(x/r) + 5(y/r)
multiply by r
r^2 = 8x + 5y
x^2 + y^2 = 8x + 5y
x^2 - 8x + y^2 - 5y = 0

This is the equation of a circle. I will assume you know how to complete the square and thus find the centre and radius.